The velocity at the end of vaneless space(state 3) is 965.92 m/s
<h3>What is centrifugal compressor?</h3>
It increases kinetic energy to the airstream using a rotating element and then converts it into potential energy in the form of pressure.
Temperature at state 2, T₂ =T₀ + c/2Cp
Substitute T₀ =450K, c=250m/s, Cp =1005, we get
T₂ =418.90K
From the velocity triangle, sinβ₂ =c₂/v₂
v₂ = 250/sin (90°-75°) = 965.92 m/s
Thus, the velocity at the end of vaneless space is 965.92 m/s.
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Not sure what you mean by "breaks in the tension" but I suspect you mean the rope will come apart if the tension in the rope exceeds 1800 N.
In the free body diagram for the 500 N weight, we have a figure Y with the net force equations
• horizontal net force:
∑ F[hor] = T₁ cos(θ) - T₂ cos(θ) = 0
• vertical net force:
∑ F[ver] = T₁ sin(θ) + T₂ sin(θ) - 500 N = 0
From the first equation, it follows that T₁ = T₂, so I'll denote their magnitude by T alone. From the second equation, we have
2 T sin(θ) = 500 N
and if the maximum permissible tension is T = 1800 N, it follows that
sin(θ) = (500 N) / (3600 N) ⇒ θ = arcsin(5/36) ≈ 7.9°
is the smallest angle the rope can make with the horizontal.
